It is occasionally desired to generate two waveforms that are mutually orthogonal, i.e. that when multiplied by each other, yield a signal of zero average value, while, when each is multiplied by itself, each yields a signal of high average value. Often this is done by choosing sinusoidal signals at disparate frequencies or by using sine and cosine waves of the same frequency. Pseudo-random codes may be used to generate orthogonal signals with frequency content extending from zero frequency to some upper frequency, and these codes have the further advantage that, by having a bivariate amplitude, they can be communicated to, through, and from a digital computer or data link. Sources of band pass (rather than base band) signals compatible with digital processing are less available.
For example, it may be desired to transmit a message over a telephone or radio channel that has a bandwidth greater than the 300 to 3000 Hz range necessary for voice communication. Signaling might be possible in a band from, for example, 5 to 8 kHz, but the use of sinusoidal tones, even with suitable filtering, could cause annoying interference. Signaling with pseudo-random codes, as will be described hereinbelow, would be more acceptable, since they sound like a hiss, rather than a distracting, clear tone. For a general discussion of digital techniques used for signaling with psseudo-random codes or noises (PRN) see, for example, Mahlon F. Easterling, "Modulation by Pseudo-random Sequences", ch. 5 of Digital Communications with Space Applications, New Jersey: Prentice-Hall, Inc., 1964.